共查询到19条相似文献,搜索用时 62 毫秒
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设d≥1为正整数,S为Rd中的单纯形,C(S)为S上连续函数类,f(x)∈C(S),f(x)≥0,f(x) 0,p>1,‖@‖p为通常的Lp范数,‖@‖为一致范数,则存在Pn(x)∈∏+n,d={Pn(x)Pn(x)=ak≥0},常数C>0使‖f-1/Pn‖p≤C[ω2φ(f,/4n)+‖f‖/n],这里对k,x∈Rd,k=(k1,k2,…,kd),x=(x1,x2,…,xd),记|k|=k1+k2+…+kd,|x|=x1+x2+…+xd,xk=xk11xk22…xk11dk22,ω24(f,t)为单纯形S上关于一致范数的二阶Ditzian-Totik光滑模. 相似文献
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设d≥1为正整数,S为Rd中的单纯形,C(S)为S上的连续函数类,f(x)∈C(S),f(x)≥0,f≠0,则文中证明存在Pn(x)∈Ⅱ+n,d={Pn(x)=∑|k|≤n akxk(1-|x|)n-|k|x∈S,ak≥ 0},绝对常数C>0使||f-1/Pn||≤C[ωψ(f,1/√n)+||f||/√n],这里k,x∈Rd,k=(k1,k2,…,kd),x=(x1,x2,…,xd),|k|=k1+k2+…+kd,|x|=x1+x2+…+xd,xk=x1k1x2k2…xdkd,ωψ(f,t)为单纯形S上的一阶Ditzian-Totik光滑模,||f||=maxx∈S|f(x)|. 相似文献
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借助于光滑模ωψ^rλ(f,t)(0≤λ≤1)给出了Bernstein算子线性组合同时逼近的点态结果。 相似文献
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一类Orlicz空间中复系数多项式的倒数逼近 总被引:1,自引:0,他引:1
定义了互余的N函数M(u)和N(v)的△条件,并研究了由这种N函数M(u)所生成的一类Orlicz空间中复系数多项式的倒数逼近问题. 相似文献
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设F(t)是表示寿命的分布函数,G(t)是表示删失的分布函数,F(t)是F(t)=1-F(t)的Kaplan-Meier估计。 相似文献
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设F(t)是表示寿命的分布函数,G(t)是表示删失的分布函数,F(t)是F(t)=1—F(t)的Kaplan-Meier估计.本文在F(t),G(t)均连续的条件下,证明了对任何取定的0<t<TH,有其中TH=inf{t:H(t)=0},H(t)=(1-F(t))(1-G(t)),渐近方差的刀切估计. 相似文献
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关于回归函数核估计的正态逼近速度 总被引:4,自引:0,他引:4
§1.引言和主要结果 设{(X_i,Y_i);1≤i≤n}为来自二元总体的iid样本。对于回归函数r(x)=E(Y|X=x)的估计问题,早在1964年,Nadaraya首先在文献[1]中提出了如下的核估计 相似文献
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Lian Hai & Garidi Wu 《分析论及其应用》2013,29(2):149-157
In order to study the approximation by reciprocals of polynomials with real coefficients, one always assumes that the approximated function has a fixed sign on the given interval. Sometimes, the approximated function is permitted to have finite sign changes, such as $l(l\geq1)$ times. Zhou Songping has studied the case $l=1$ and $l\geq2$ in $L^{p}$ spaces in order of priority. In this paper, we studied the case $l\geq2$ in Orlicz spaces by using the function extend, modified Jackson kernel, Hardy-Littlewood maximal function, Cauchy-Schwarz inequality, and obtained the Jackson type estimation. 相似文献
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Pointwise Approximation Theorems for Combinations
and Derivatives of Bernstein Polynomials 总被引:1,自引:0,他引:1
Lin Sen XIE 《数学学报(英文版)》2005,21(5):1241-1248
We establish the pointwise approximation theorems for the combinations of Bernstein polynomials by the rth Ditzian-Totik modulus of smoothness wФ^r(f, t) where Ф is an admissible step-weight function. An equivalence relation between the derivatives of these polynomials and the smoothness of functions is also obtained. 相似文献
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We discuss whether or not it is possible to have interpolatory pointwise estimates in the approximation of a function f∈ C[0,1] , by polynomials. For the sake of completeness, as well as in order to strengthen some existing results, we discuss briefly
the situation in unconstrained approximation. Then we deal with positive and monotone constraints where we show exactly when
such interpolatory estimates are achievable by proving affirmative results and by providing the necessary counterexamples
in all other cases.
November 16, 1998. Date revised: July 12, 1999. Date accepted: September 13, 1999. 相似文献
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Lin Sen XIE Zhong Rui SHI 《数学学报(英文版)》2007,23(5):935-944
In this paper, we investigate the relation between the rate of convergence for the derivatives of the combinations of Baskakov operators and the smoothness for the derivatives of the functions approximated. We give some direct and inverse results on pointwise simultaneous approximation by the combinations of Baskakov operators. We also give a new equivalent result on pointwise approximation by these operators. 相似文献
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本文应用Ditzian-Totik模得到Baskakov-Durrmeyer算子线性组合的点态逼近的等 价定理. 相似文献
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本文给出了Szász-Mirakjan算子线性组合的点态逼近定理。另外,还研究了Szász-Mirakjan算子高阶导数与所逼近函数光滑性之间的关系。 相似文献
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Recently, Li [16] introduced three kinds of single-hidden layer feed-forward
neural networks with optimized piecewise linear activation functions and fixed
weights, and obtained the upper and lower bound estimations on the approximation
accuracy of the FNNs, for continuous function defined on bounded intervals. In the
present paper, we point out that there are some errors both in the definitions of the
FNNs and in the proof of the upper estimations in [16]. By using new methods, we
also give right approximation rate estimations of the approximation by Li’s neural
networks. 相似文献
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研究Bernstein-Sikkema算子的逼近问题,得到强型正定理和弱型逆定理,改进了文献[1]的结果 相似文献